Can you find out the missing number in the grid?

Buy me, smell me or deliver me, I do not change.

Who am I?

Can you figure out the logic I used to decide the order of the following words:
gun, shoe, spree, door, hive, kicks, heaven, gate, line, den

In a university, a professor gave a set of three problems to the three brilliant students of his class. See the image for the questions.

The below given figure comprises of a pattern through which you can determine the missing letter. Can you push your mind to find the pattern and add the missing letter?

What jumps when it walks and sits when it stands?

Luis Garavito killed Density x Volume.

Who is Luis Garavito ?

What happened when the wheel was invented?

I have four wings but can't fly.
I express no emotions.
I am found on the exact spot every time you look.
I keep toiling away with a little sound.

Do you know what am I?

I am a five-letter word and people eat me. If you remove the first letter I become an energy form. If you remove the first two letters, I am needed to live. Scramble the last three letters and I am a drink. What word am I?